Continuing Problem 6, suppose the company is selling in the United States, the United Kingdom, and Japan. Assume the unit production cost is $50, and the exchange rates are 1.22 ($/£) and 0.00965 ($/¥). Each country has its own constant elasticity demand function. The parameters for the United States are 19,200,000 and −2; the parameters for the United Kingdom are 10,933,620 and −2.2; and the parameters for Japan are 15,003,380,400 and −1.9. The company has a production capacity of 3000. Therefore, the company can sell only as many units, in total, to all three countries as it can produce. a. Develop a spreadsheet model that determines the prices the company should charge and the numbers of units it should sell in each of the three countries to maximize its total profit in dollars. (Note that if total demand is greater than capacity, the company has to decide how much to sell in each country. Therefore, the amounts to sell become decision variables.) b. When the capacity is 3000, is all of this capacity used? Answer the same question if the capacity is increased to 4000. c. Discuss the customer behavior that might result from the solution to the model in part a. If the company sets its price in one country relatively low compared to its price in another country, what might customers do? 7.2 Pricing with Exchange Rate Considerations At Madison We continue Example 7.1 but now assume that Madison manufactures its product in the United States and sells it in the United Kingdom (UK). Given the prevailing exchange rate in dollars per pound. Madison wants to determine the price in pounds it should charge in the UK so that its profit in dollars is maximized. The company also wants to see how the optimal price and the optimal profit depend on exchange rate fluctuations. 7.1 Pricing Decisions at Madison The Madison Company manufactures and retails a certain product. The company wants to determine the price that maximizes its profit from this product. The unit cost of producing and marketing the product is $50. Madison will certainly charge at least $50 for the product to ensure that it makes some profit. However, there is a very competitive market for this product, so that Madison’s demand falls sharply when it increases its price. How should the company proceed? 2 In the exchange rate model in Example 7.2, suppose the company continues to manufacture its product in the United States, but now it sells its product in the United States, the United Kingdom, and possibly other countries. The company can independently set its price in each country where it sells. For example, the price could be $150 in the United States and £110 in the United Kingdom. You can assume that the demand function in each country is of the constant elasticity form, each with its own parameters. The question is whether the company can use Solver independently in each country to find the optimal price in this country. (You should be able to answer this question without actually running any Solver model(s), but you might want to experiment, just to verify your reasoning.)

BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
BuyFind

Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

Solutions

Chapter
Section
Chapter 7.3, Problem 13P
Textbook Problem

Continuing Problem 6, suppose the company is selling in the United States, the United Kingdom, and Japan. Assume the unit production cost is $50, and the exchange rates are 1.22 ($/£) and 0.00965 ($/¥). Each country has its own constant elasticity demand function. The parameters for the United States are 19,200,000 and −2; the parameters for the United Kingdom are 10,933,620 and −2.2; and the parameters for Japan are 15,003,380,400 and −1.9.

The company has a production capacity of 3000. Therefore, the company can sell only as many units, in total, to all three countries as it can produce.

  1. a. Develop a spreadsheet model that determines the prices the company should charge and the numbers of units it should sell in each of the three countries to maximize its total profit in dollars. (Note that if total demand is greater than capacity, the company has to decide how much to sell in each country. Therefore, the amounts to sell become decision variables.)
  2. b. When the capacity is 3000, is all of this capacity used? Answer the same question if the capacity is increased to 4000.
  3. c. Discuss the customer behavior that might result from the solution to the model in part a. If the company sets its price in one country relatively low compared to its price in another country, what might customers do?

7.2 Pricing with Exchange Rate Considerations At Madison

We continue Example 7.1 but now assume that Madison manufactures its product in the United States and sells it in the United Kingdom (UK). Given the prevailing exchange rate in dollars per pound. Madison wants to determine the price in pounds it should charge in the UK so that its profit in dollars is maximized. The company also wants to see how the optimal price and the optimal profit depend on exchange rate fluctuations.

7.1 Pricing Decisions at Madison

The Madison Company manufactures and retails a certain product. The company wants to determine the price that maximizes its profit from this product. The unit cost of producing and marketing the product is $50. Madison will certainly charge at least $50 for the product to ensure that it makes some profit. However, there is a very competitive market for this product, so that Madison’s demand falls sharply when it increases its price. How should the company proceed?2

In the exchange rate model in Example 7.2, suppose the company continues to manufacture its product in the United States, but now it sells its product in the United States, the United Kingdom, and possibly other countries. The company can independently set its price in each country where it sells. For example, the price could be $150 in the United States and £110 in the United Kingdom. You can assume that the demand function in each country is of the constant elasticity form, each with its own parameters. The question is whether the company can use Solver independently in each country to find the optimal price in this country. (You should be able to answer this question without actually running any Solver model(s), but you might want to experiment, just to verify your reasoning.)

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Chapter 7 Solutions

Practical Management Science
Ch. 7.3 - ELECTRICITY PRICING AT FLORIDA POWER AND LIGHT...Ch. 7.3 - In the electricity pricing model in Example 7.4,...Ch. 7.3 - Continuing Problem 6, suppose the company is...Ch. 7.3 - PRICING SUITS AT SULLIVANS Sullivans is a retailer...Ch. 7.3 - Continuing the previous problem (the model in part...Ch. 7.4 - In estimating the advertising response function in...Ch. 7.4 - The best-fitting advertising response function in...Ch. 7.4 - In judging the fit of the estimated response...Ch. 7.4 - Starting with the solution to the advertising...Ch. 7.4 - The preceding problem indicates how fewer...Ch. 7.4 - In the solution to the advertising selection model...Ch. 7.4 - The advertising response function in Equation...Ch. 7.4 - In Example 7.5, we implied that each of the five...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.5 - The Lafferty Company wants to locate a warehouse...Ch. 7.6 - The file P07_28.xlsx lists the scores of all NFL...Ch. 7.6 - Carry out the suggestion in Modeling Issue 3. That...Ch. 7.6 - Carry out the suggestion in Modeling Issue 2 for...Ch. 7.6 - The file P07_31.xlsx contains scores on all of the...Ch. 7.6 - By the time you are reading this, the 2016 NFL...Ch. 7.6 - By the time you are reading this, the 20162017 NBA...Ch. 7.6 - The method for rating teams in Example 7.8 is...Ch. 7.7 - For each of the following, answer whether it makes...Ch. 7.7 - Add a new stock, stock 4, to the model in Example...Ch. 7.7 - In the model in Example 7.9, stock 2 is not in the...Ch. 7.7 - The stocks in Example 7.9 are all positively...Ch. 7.7 - The file P07_39.xlsx contains historical monthly...Ch. 7.7 - This problem continues using the data from the...Ch. 7.7 - Continuing the previous problem, find the...Ch. 7.7 - In many cases, the portfolio return is at least...Ch. 7.8 - Given the data in the file Stock Beta.xlsx,...Ch. 7.8 - Solve the previous problem, but analyze GE instead...Ch. 7 - Suppose Ford currently sells 250,000 Ford Mustangs...Ch. 7 - Suppose the current exchange rate is 115 yen per...Ch. 7 - Another way to derive a demand function is to...Ch. 7 - A company produces widgets at plants 1 and 2. It...Ch. 7 - If a monopolist produces q units, she can charge...Ch. 7 - It costs a company 15 to purchase an hour of labor...Ch. 7 - In the previous problem, what is the minimum-cost...Ch. 7 - The cost per day of running a hospital is 300,000...Ch. 7 - Two companies are producing widgets. It costs the...Ch. 7 - A company manufactures two products. If it charges...Ch. 7 - A brewing company has 100,000 to spend on...Ch. 7 - QH Company advertises during soap operas and...Ch. 7 - A beer company has divided Bloomington into two...Ch. 7 - A company uses raw material to produce two...Ch. 7 - JJ has given you 12 million to spend on...Ch. 7 - Based on Kolesar and Blum (1973). Suppose that a...Ch. 7 - A company has five factories. The x- and...Ch. 7 - Monroe County is trying to determine where to...Ch. 7 - Consider three investments. You are given the...Ch. 7 - You have 50,000 to invest in three stocks. Let Ri...Ch. 7 - An oil company must determine how many barrels of...Ch. 7 - Suppose that you are hiring a weather forecaster...Ch. 7 - The cost of producing x units of a product during...Ch. 7 - Four items are for sale in the Dollar Value store....Ch. 7 - Most economies have a goal of maximizing the...Ch. 7 - Each morning during rush hour, 10,000 people want...Ch. 7 - Based on Grossman and Hart (1983). A salesperson...Ch. 7 - Find the minimum perimeter rectangle having area...Ch. 7 - You are given that the two nonhypotenuse sides of...Ch. 7 - A cylindrical soda can has a volume of 20 cubic...Ch. 7 - City B is 10 miles downstream from city A. City A...Ch. 7 - You can swim two miles per hour and run six miles...Ch. 7 - A triangle has a 5-inch side and a 12-inch side....Ch. 7 - Your company is about to market a new golf club....Ch. 7 - For the product mix examples (Examples 3.1 and 3.2...Ch. 7 - For the oil blending example (Example 4.4 in...Ch. 7 - For the aggregate planning example (Example 4.3 in...Ch. 7 - Consider the sports ratings model in section 7.6....Ch. 7 - Consider the sports ratings model in section 7.6....Ch. 7 - UE is going to invest 400 million to acquire...Ch. 7 - Your family owns a large farm that can grow wheat,...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...Ch. 7 - GMS Stock Hedging Kate Torelli, a security analyst...

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